I have a Fisher-Price baby swing that my 7-week-old is spending a lot of time in :) I've found that I often put him in wide awake, and a short while later he's soundly sleeping. Is it ok to leave him asleep in the swing? Is there any reason to move him to a crib or bassinet?

7 weeks seems young to me to fall asleep in anything other than a crib, although most of my concern comes from my wife's wheedling about shaking babies. She's overboard on what constitutes shaking, but until our kids sat upright if they fell asleep they always got moved to the crib. Now at 14 months our youngest takes lots of naps in the swing.
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MichaelFJun 16 '11 at 12:53

2

My daughter napped and on a couple of occasions spent the night in a very similar swing until she was ~5 months old. I don't think it hurt her any.
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stojJun 16 '11 at 15:06

When our son was an infant, he loved to swing in the infant car seat (safely suspended in a door frame using hooks and ropes), and often fell asleep in it. Since the infant car seat is made to provide a safe and comfortable position for the baby, we had no concerns about him sleeping in it. But we often moved him from the seat to his crib in the bedroom once he was sleeping deeply, mostly out of practical considerations - the car-seat-swing blocked the doorway :) and we had to be rather quiet.

Updates:

The swing you're linking to in your comment provides a somewhat upright position. Be aware that most physiotherapists (source: I'm married to one) will tell you that infants should not be upright until they can sit on their own - before that, the spine and upper body is not sufficiently developed to support the weight of the head and body. So if your swing allows leaning the child back to (almost?) flat, it would be better.

The infant car seat also has a somewhat upright seating position, so we tried to make sure it was leaned as far back as possible.

How flat is flat? That depends on how much you believe the physio arguments. Again based on my wife's comments, I'd say the spine/back should be angled no more than 15-20 degrees above level, but this is not at all an exact statement! I think the underlying idea is to avoid a lengthwise compression in the spine.

the swing has a "recline" feature so that you can move the seat back... how do I know if this is flat enough or considered upright?
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babiesRyummyJun 16 '11 at 10:03

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Our daughter slept in her swing until she was too tall for it (around 6 months). As a newborn (<3 months) she slept a LOT in her swing and seemed to love it - we had it on the maximum recline until she could sit upright. ("flat enough" = they aren't forced to hold their head up). Be absolutely SURE to get into the habit of buckling your kid in. We were lazy in the beginning and didn't use to put the shoulder straps on - but they grow fast, and it might be too late before you realize that you need shoulder straps. Start getting into the habit NOW to buckle them in FULLY.
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SwatiJun 16 '11 at 14:49

My mom worried about us leaving the kid in a swing because of the saggy/bowed shape of the seat. Her point was that it could negatively affect the baby's spine. So we listened to her and now try to keep the baby on a flat surface while he's sleeping.

I used a similar swing (Boppy) which allowed for my son to be a little more reclined than the FP one you have. As long as his head isn't flopping around and he can't fall out of it, having him in the swing won't hurt him.

I can see your FP swing also has a neck support for infants, that's good - if it reclines more, then it'll be even better for him.

As a side note: My son was visiting his farmor today (grandmother) and she had the swing out for her other grandson to use... but Matthias got to it first (at 3 years old) and took a nap in it with it running.

We had a Graco baby swing similar to the one in the picture below, and all 3 of our boys periodically fell asleep in it with no side effects. It has a four-point harness but no particular head or neck support. I'd say your swing looks better for sleeping in.

We used a Graco swing a lot like this one and on some rough nights where Eli would not sleep in the crib we were able to get him to fall asleep in the swing. It saved our sanity a number of times. Ours had a choice of music, ocean waves, and a very creepy heart beat sound, he like each one of them at one time or another.
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Dave NelsonAug 6 '12 at 19:08